Obtaining a strong and reproducible surface-enhanced Raman scattering (SERS) signal with a narrow distribution of the high SERS enhancement factor (EF) values from the plasmonic nanostructures is critical for better understanding and practical use of the single-molecule SERS (SMSERS) nanoprobes. In this regard, the systematic and thorough studies about the relationships between single-molecule SERS intensity, EF distribution over many particles, inter-particle distance, particle size/shape/composition and excitation laser wavelength are needed. Here, we extensively studied these relationships using the single-particle AFM-correlated Raman measurement method with two different single-DNA-tethered Au-Ag core-shell nanodumbbell (GSND) designs with engineerable nanogap - the GSND-I with various inter-particle nanogaps from ~4.8 nm to <1 nm or with no gap and the GSND-II with the fixed inter-particle gap size and varying particle size for various size of GSND-II particles from a 23 nm-30 nm pair to a 50 nm-60 nm pair. From the GSND-I probes, we learned that synthesizing <1 nm gap is a key to obtain strong SMSERS signals with a narrow EF value distribution. Importantly, in the case of the GSND-I with <1 nm inter-particle gap, an EF value of as high as 5.9×1013 (average value = 1.8×1013) was obtained and the EF values of analyzed particles were narrowly distributed between 1.9×1012 and 5.9×1013. In the case of the GSND-II probes, a combination of >50 nm Au cores and 514.5 nm laser wavelength that matches well with Ag shell generated stronger SMSERS signals with a more narrow EF distribution than <50 nm Au cores with 514.5 nm laser or the GSND-II structures with 632.8 nm laser. Our results show the usefulness and flexibility of these GSND structures in studying and obtaining SMSERS structures with a narrow distribution of high EF values and the GSNDs are promising SERS probes with highly sensitive and quantitative detection capability when optimally designed.